Hostname: page-component-586b7cd67f-vdxz6 Total loading time: 0 Render date: 2024-11-22T23:50:46.309Z Has data issue: false hasContentIssue false
  • English
  • Français

Conformal mapping techniques for the modelling of liquid crystal devices

Published online by Cambridge University Press:  24 January 2011

A. J. DAVIDSON  and
N. J. MOTTRAM
A. J. DAVIDSON
Affiliation:
Department of Mathematics and Statistics, University of Strathclyde, 26 Richmond Street, Glasgow G1 1XH, UK email: [email protected]
N. J. MOTTRAM
Affiliation:
Department of Mathematics and Statistics, University of Strathclyde, 26 Richmond Street, Glasgow G1 1XH, UK email: [email protected]
Get access Rights & Permissions [Opens in a new window]

Abstract

In this paper, we review a number of uses of conformal mapping techniques for obtaining director profiles of liquid crystals in confined and semi-confined geometries. In particular, we will consider geometries which allow more than one stable state, some of which are of use in bistable displays. These solutions also allow the investigation of the energy of stable states and enable conclusions to be reached as to how such geometries may be optimised for bistable display applications. Such techniques are also able to provide initial configurations for the solution of more complicated situations where numerical methods are used to investigate switching characteristics.

Keywords

Liquid crystalselasticityconformal mappingbistablility
Type
Papers
Information
European Journal of Applied Mathematics , Volume 23 , Issue 1: Liquid Crystals , February 2012 , pp. 99 - 119
Copyright
Copyright © Cambridge University Press 2011

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

[1]Atluri, S. N. & Zhu, T. (1998) A new meshless local petrov-galerkin (MLPG) approach in computational mechanics. Comput. Mech. 22, 117–127.CrossRefGoogle Scholar
[2]Barberi, R., Martinot-Lagarde, P., Durand, G. & Giocondo, M. (1994) U.S. Patent No. 5357358.Google Scholar
[3]Barbero, G. (1981) On the critical angle of a NLC cell. Lett. Nuovo Cimento 32, 60–64.Google Scholar
[4]Barbero, G. & Scaramuzza, N. (1982) On the interface substrate-nematic - anchoring energy and topography. Lett. Nuovo Cimento 34, 173–179.CrossRefGoogle Scholar
[5]Bartolino, R., Li, J., Barberi, R., Dozov, I., Durand, G. & Giocondo, M. (1999) U.S. Patent No. 5995173.Google Scholar
[6]Bryan-Brown, G. P., Brown, C. V. & Jones, J. C. (1995) UK patent GB2318422.Google Scholar
[7]Bryan-Brown, G. P., Brown, C. V. & Jones, J. C. (2001) U.S. Patent No. 6249332.Google Scholar
[8]Carbone, G., Lombardo, G. & Barberi, R. (2009) Mechanically induced biaxial transition in a nanoconfined nematic liquid crystal with a topological defect. Phys. Rev. Lett. 103, 167801.CrossRefGoogle Scholar
[9]Clark, N. A. & Lagerwall, S. T. (1980) Submicrosecond bistable electro-optic switching in liquid-crystals. Appl. Phys. Lett. 36, 899–901.Google Scholar
[10]Davidson, A. J. & Mottram, N. J. (2002) Flexoelectric switching in a bistable nematic device. Phys. Rev. E 65, 051710.Google Scholar
[11]Davidson, A. J., Brown, C. V., Mottram, N. J., Ladak, S. & Evans, C.R. (2010) Defect trajectories and domain-wall loop dynamics during two-frequency switching in a bistable azimuthal nematic device. Phys. Rev. E 81, 051712.CrossRefGoogle Scholar
[12]Discoll, T. A. & Trefethen, L. N. (2002) Schwarz-Chrtistoffel Mapping, Cambridge University Press, Cambridge, UK.Google Scholar
[13]Dozov, I. & Durand, G. (1999) Surface controlled nematic bistability. Pramana-J. Phys. 53, 25–35.CrossRefGoogle Scholar
[14]de Gennes, P. G. & Prost, J. (1993) The Physics of Liquid Crystals, 2nd ed., Clarendon Press, Oxford.CrossRefGoogle Scholar
[15]Ivanov, V. I. & Trubetskov, M. K. (1995) Handbook of Conformal Mapping with Computer-Aided Visualization, CRC Press, Boca Raton, USA.Google Scholar
[16]Kitson, S. & Geisow, A. (2002) Controllable alignment of nematic liquid crystals around microscopic posts: Stabilization of multiple states. Appl. Phys. Lett. 80, 3635–3637.CrossRefGoogle Scholar
[17]Ladak, S., Davidson, A. J., Brown, C. V., & Mottram, N. J. (2009) Sidewall control of static azimuthal bistable nematic alignment states. J. Phys. D - Appl. Phys. 42, 085114.Google Scholar
[18]Lagerwall, S. T. (1999) Ferroelectric and Antiferroelectric Liquid Crystals, Wiley, New York.Google Scholar
[19]Majumdar, A., Newton, C. J. P., Robbins, J. M. & Zyskin, M. (2007) Topology and bistability in liquid crystal devices. Phys. Rev. E 75, 051703.Google Scholar
[20]Mottram, N. J., Ramage, A., Kelly, G. & Davidson, A. J. (2006) UK patent GB20040026582.Google Scholar
[21]Newton, C. J. P. & Spiller, T. P. (1997) Bistable nematic liquid-crystal device modeling. In: SID Proceedings of IDRC '97 SID, Santa Ana, CA, USA, pp. 13–16.Google Scholar
[22]Schopohl, N. & Sluckin, T. J. (1987) Defect core structure in nematic liquid-crystals. Phys. Rev. Lett. 59, 2582–2584.CrossRefGoogle ScholarPubMed
[23]Spencer, T. J. & Care, C. M. (2006) Lattice boltzmann scheme for modeling liquid-crystal dynamics: Zenithal bistable device in the presence of defect motion. Phys. Rev. E 74, 061708.Google Scholar
[24]Spiegel, M.R. (1964) Complex Variables with an Introduction to Conformal Mapping and its Applications, Schaum's Outlines Series, McGraw-Hill.Google Scholar
[25]Towler, M. J., Bryan-Brown, G. P., McDonnell, D. G. & Brancroft, M. S. (1999) U.S. Patent No. 5796459.Google Scholar
[26]Tsakonas, C., Davidson, A. J., Brown, C. V. & Mottram, N. J. (2007) Multistable alignment states in nematic liquid crystal filled wells. Appl. Phys. Lett. 90, 111913.CrossRefGoogle Scholar
[27]Uche, C., Elston, S. J. & Parry-Jones, L.A. (2006) Modelling zenithal bistability at an isolated edge in nematic liquid crystal cells. Liq. Cryst. 33, 697–704.Google Scholar
[28]Wojtowicz, P. J., Priestly, E. B. & Sheng, P. (1976) Introduction to Liquid Crystals, Plenum Press, New York and London.Google Scholar